Countably regular good spaces and almost Cκ-spaces
Submitted: 2024-06-30
|Accepted: 2024-11-14
|Published: 2025-04-01
Copyright (c) 2025 Arash Hayati, Mehrdad Namdari, Somayeh Soltanpour
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
Functionally countable subalgebra, space of countable pseudocharacter, almost-resolvable space, CUC-space, CRG-space, almost Cκ-Baire space, almost CP-point, almost CP-space
Supporting agencies:
Shahid Chamran University of Ahvaz
Abstract:
In this paper, we build upon our previous studies by redefining fundamental concepts and transferring them from rings of continuous functions to rings of continuous functions with countable images. This article will focus on regular good spaces (``"RG-spaces", for short) and related concepts. Specifically, we introduce and examine two generalizations of RG-spaces, calling countably regular good spaces and strongly countably regular good spaces.
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